Engr 123
Assignment 2
Day of the Week
January 20, 2016
Due: January 27, 2016
Charles Dodgson, aka Lewis Carroll of Alice in Wonderland fame, was a mathematician
who taught at Oxford in the 19th century. He published an algorithm which allows a user
to determine the day of the week for any given date. His algorithm is given below.
A given date has four parts: the century, the year, the month, and the date. Each of these
four items is processed separately to form a number. When the numbers are added the
sum modulo seven provides the day of the week of the date with Sunday = 0, Monday =1,
etc.
Century number:
The century number is 2 x (3 - century mod 4). For example, if the date is January
21, 2009, the century is 20 so 2 x (3 – 20%4) = 6.
Year number:
The year number is ((int) year/12) + (year mod 12) + (int)((year mod 12) /4). For
example if the date is January 21, 2009 the year is 9 so (int)9/12 + 9%12 +
(int)(9%12)/4) = 0 + 9 + 2 = 11.
Month number:
The month number is given by the following table:
Month Num
Month
January
0
July
February
3
August
March
3
September
April
6
October
May
8
November
June
4
December
For the date January 21, 2009 the month number is 0.
Num
6
2
5
0
3
12
Date number:
The day number is the day of the month. For example, if the date is January 21, 2009
the day number is 21.
Leap Year Correction:
All years that are evenly divisible by 400 or, are evenly divisible by 4 and not evenly
divisible by 100 are leap years. So that 2000 is evenly divisible by 400 so it is a
leap year. The year 2004 is evenly divisible by 4 and it is not evenly divisible by
100 so it is also a leap year. If the month is January or February in a leap year
you must subtract 1 from the total unless the total is 0 in which case you must add
6.
For the date January 21, 2009, the year is not a leap year so no correction is
necessary. The total of the four numbers is 6 + 11 + 0 + 21 = 38. 38 % 7 = 3 so
the day is Wednesday.
More examples:
March 31, 2009
The century number is 2 x (3 - century mod 4). The century is 20 so 2 x (3 – 20%4) = 6.
The year number is ((int) year/12) + (year mod 12) + (int)((year mod 12) /4). So
(int)9/12 + 9%12 + (int)(9%12)/4) = 0 + 9 + 2 = 11.
The month number is 3 from the table.
The day number is 31.
The total is 6 + 11 + 3 + 31 = 51 51%7 = 2 so Tuesday
December 25, 2008
The century number is 2 x (3 - century mod 4). The century is 20 so 2 x (3 – 20%4) = 6.
The year number is ((int) year/12) + (year mod 12) + (int)((year mod 12) /4). So
(int)8/12 + 8%12 + (int)(8%12)/4) = 0 + 8 + 2 = 10.
The month number is 12 from the table.
The day number is 25.
The total is 6 + 10 + 12 + 25 = 53 53 % 7 = 4 so Thursday
September 18, 1783
The century number is 2 x (3 - century mod 4). The century is 17 so 2 x (3 – 17%4) = 4.
The year number is ((int) year/12) + (year mod 12) + (int)((year mod 12) /4). So
(int)83/12 + 83%12 + (int)(83%12)/4) = 6 + 11 + 2 = 19.
The month number is 5 from the table.
The day number is 18.
The total is 4 + 19 + 5 + 18 = 46, 46 % 7 = 4 so Thursday
Write a console application in C# which will print the day of the week in response to the
entry of a date. Your date may be entered on three lines using three prompts to the user.
A typical output for your program is shown below: Note that the program continues to
prompt the user for dates until the user enters the word "Done" for the month.
Enter the month: December
Enter the day of the month: 25
Enter the year: 2008
The day for December 25, 2008 is Thursday.
Enter the month: Done
After you get your program running correctly, place a copy of the design into the project
folder as a doc or docx file. Right click on the project folder and choose Send To →
Compressed zip file. Rename the compressed zip file as Asn02XXX.zip where XXX are
you three initials. Upload the renamed file to \\cecsfp01\users\everyone\engr123.